Estimating the Effective Reproduction Number of COVID-19 in South Africa
Louis Rossouw
2021-03-28
1 Introduction
This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 02db0f525a288673aba4923c6b88677071850d51.
2 Data
Case data is captured from the NICD National COVID-19 Daily Report [3]. This contains the daily cases reported by the NICD for South Africa by province. Data is shown by specimen reported date. Most recent data is excluded due to incomplete reporting of tests in last number of days.
The following fixes are applied:
- Calculate daily new cases from cumulative data captured.
- Add a total for South Africa as a whole.
- Add records (with 0 case count) in periods where no cases were recorded.
- Recalculate cumulative figures.
- Data captured for speciments reported in the 3 days before the reporting date is excluded due as cases reporting is likely incomplete. In future versions of this report this may be changed.
3 Methodology
The methodology is described in detail here.
4 Results
4.1 Cases
Below a 7-day moving average daily case count is plotted by province on a log scale since start of the epidemic:
Below the above chart is repeated for the last 30-days:
4.2 Current \(R_{t,m}\) estimates by Province
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| province | Count (Week) | Week Ending | Reproduction Number [95% Confidence Interval] |
|---|---|---|---|
| Eastern Cape | 119 | 2021-03-24 | 0.9 [0.76 - 1.08] |
| Free State | 772 | 2021-03-24 | 1.0 [0.95 - 1.10] |
| Gauteng | 1,942 | 2021-03-24 | 0.9 [0.90 - 0.99] |
| KwaZulu-Natal | 679 | 2021-03-24 | 0.7 [0.64 - 0.76] |
| Limpopo | 178 | 2021-03-24 | 0.9 [0.78 - 1.06] |
| Mpumalanga | 784 | 2021-03-24 | 0.9 [0.84 - 0.97] |
| North West | 637 | 2021-03-24 | 0.9 [0.86 - 1.01] |
| Northern Cape | 615 | 2021-03-24 | 0.9 [0.83 - 0.98] |
| Western Cape | 935 | 2021-03-24 | 1.0 [0.94 - 1.07] |
| South Africa | 6,661 | 2021-03-24 | 0.9 [0.89 - 0.94] |
Estimated Effective Reproduction Number by Province
4.3 Maps of Effective Reproduction Number
Below estimates of the reproductive number is plotted on maps of South Africa [4].
Estimated Effective Reproduction Number Based on Cases by Province
4.4 Estimated Effective Reproduction Number for South Africa over Time
Below the results for South Africa ove the last 90 days is plotted.
Estimated Effective Reproduction Number Based on Cases for South Africa over Time
4.5 Map of Effective Reproduction Number Over Last 60 Days
Below the reproduction number by week by province is animated:
4.6 Estimated Effective Reproduction Number for Provinces over Time
The results for each province over last 90 days is plotted below.
4.6.1 Eastern Cape
Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time
4.6.2 Free State
Estimated Effective Reproduction Number Based on Cases for Free State over Time
4.6.3 Gauteng
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
4.6.4 KwaZulu-Natal
Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time
4.6.5 Limpopo
Estimated Effective Reproduction Number Based on Cases for Limpopo over Time
4.6.6 Mpumalanga
Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time
4.6.7 Northern Cape
Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time
4.6.8 North West
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
4.6.9 Western Cape
Estimated Effective Reproduction Number Based on Cases for Western Cape over Time
4.7 Detailed Results
Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.
5 Discussion
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
- It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
- It relies on an assumed generation interval assumptions.
- The size of the time window can affect the volatility of results.
- Results are time lagged with regards to true infection.
- It’s sensitive to changes in case detection.
- The generation interval may change over time.
Further to the above the estimates are made under assumption that the cases are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred earlier. These figures have not been shifted back.
Despite these limitation it is believed that the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
Having said all the above it would appear that the effective reproduction number was reasonably high in South Africa from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.
References
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133.
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013.
[3] National Institute for Communicable Diseases, “National COVID-19 Daily Report,” 2021.
[4] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018.